This disclosure pertains to microlithography, which is a key technology used in the manufacture of micro-electronic devices such as semiconductor integrated circuits, displays, and the like. More specifically, the disclosure pertains to methods for predicting the respective profiles of pattern elements, as projected onto a resist layer of a microlithographic substrate, after development of the resist.
During projection microlithography, a pattern (usually comprising an enormous number of pattern elements) defined on a reticle is projected by the beam onto the surface of a suitable substrate such as a semiconductor wafer. So as to be imprintable with an image of the projected pattern, the upstream-facing surface of the substrate is coated with a suitable exposure-sensitive material, termed a xe2x80x9cresist.xe2x80x9d Especially with patterns comprised of extremely small elements, the shapes (profiles) of individual elements as projected onto the substrate frequently differ from respective design-mandated profiles for the elements. These changes in profile can yield less than satisfactory microlithographic results. Hence, before patterns actually are projection-exposed, simulations desirably are performed to predict the as-printed profiles of the pattern elements.
In charged-particle-beam (CPB) microlithography (e.g., electron-beam microlithography) the conventional method for estimating the as-printed profiles of pattern elements is an extensive calculation based on the spatial distribution of exposure energy accumulated in the exposed resist at the time of resist development. The calculation is based on the well-known Monte Carlo simulation method, in which method the trajectories of electrons scattered within the resist are simulated by assigning directions to the trajectories according to random numbers. The electrons are assumed to undergo scattering events due to elastic interactions with atoms in molecules of the resist, wherein each scattering event results in loss of energy of the participating electron. The scattering events also result in corresponding xe2x80x9cexposurexe2x80x9d reactions involving the molecules of the resist. The resulting local accumulation of exposure energy within the resist due to the scattering electrons is calculated, and the cumulative exposure-energy data are converted to corresponding local rates of resist xe2x80x9cdevelopment.xe2x80x9d The development calculation is performed (e.g., by a string method) using the resulting spatial distribution of the rate of resist development, yielding predictions of corresponding profiles of pattern elements after resist development. This method is described in xe2x80x9cLine-Profile Resist Development Simulation Techniques,xe2x80x9d Polymer Eng. Sci. 17:381 (1977).
However, with increasing demand for ever-smaller sizes of critical circuit elements in microelectronic devices, a need has arisen not only for predictions of the cross-sectional (two-dimensional) profiles of pattern elements realized after resist development but also for predictions of three-dimensional (xe2x80x9c3Dxe2x80x9d or xe2x80x9cbird""s-eyexe2x80x9d) profiles. To produce a 3D profile using a conventional Monte Carlo simulation in which scattering is simulated using random numbers requires an extremely long calculation time and use of a computer having an extremely large memory.
As a result, investigations of alternative calculation techniques have been investigated, such as making a respective table of the spatial distribution of cumulative exposure energy (an xe2x80x9cExposure Intensity Distributionxe2x80x9d or xe2x80x9cEIDxe2x80x9d function) after calculating the scattering of electrons entering the resist at a given point. Each table is stored in memory and recalled as required for fitting to a simple function so as to compress the volume of data. For example, see Kobinata et al., xe2x80x9cProximity Effect by Pattern-Modified Stencil Mask in Large-Field Projection Electron-Beam Lithography,xe2x80x9d Jpn. J Appl. Phys. 37:6767 (1998). According to this paper, in a deceleration region of about 10 keV in the resist, if the EID function is expressed as a linear sum of two Gaussian distributions, the calculated results agree well with actual exposure results.
The spatial distribution of cumulative exposure energy over the entire resist is determined by calculations in which the EID function is superimposed over the entire resist. The resulting cumulative-energy data are converted to corresponding resist-development rates. But, this conversion involves using a simple analytical formula that only roughly approximates the chemical reaction involved in development of the particular resist. Furthermore, the parameters of the analytical formula are adjusted suitably to simplify the calculation.
Recently, there has been a much-increased demand for resist-development simulations that can predict accurately the development behavior of very fine pattern elements (e.g., elements having linewidths of 100 nm or less) projected onto the resist. Under these conditions, prediction of as-developed profiles of pattern elements conventionally cannot be performed with sufficient accuracy, even by using resist-development models that approximate development of the well-understood polymethylmethacrylate (PMMA) resists (which conventionally are used as positive resists) or by the Mack formula (known to be useful for chemically enhanced resists). These obstacles also exist for negative resists. For example, the edge of an actual pattern element having these dimensions, as printed in a developed resist, frequently is distorted by irregularities in the pattern-element edge (i.e., by xe2x80x9cedge roughnessxe2x80x9d) and hence has an irregular profile. But, because conventional resist-development simulations produce smooth edges, actual effects of edge roughness are not appropriately reflected in the simulation results.
In view of the shortcomings of conventional simulation methods, the present invention provides, inter alia, simulation methods that more closely approximate the profiles of projection-transferred pattern elements as formed in the resist after exposure and resist development.
According to one aspect of the invention, methods are provided for simulating the profiles of pattern elements as projection-exposed onto a layer of resist, wherein the methods yield estimates of the cross-sectional post-development profile of the resist along edges of pattern elements. The simulation includes a calculation based on the two-dimensional distribution of the rate of resist development. In a first step of the method, with respect to a layer of the resist, data are input concerning the distribution of molecular weight and of mean density of the resist. In a second step, from the input data, a volume distribution of molecules of the resist is calculated. In a third step, a line (extending along a resist cross-section and indicating a line of contact of the surface of the resist with a resist-developer solution) is divided into increments desirably having equal respective lengths. In a fourth step, based on the distribution of development rate for the resist, respective weighting parameters are assigned to each increment. In a fifth step, after a selected amount of resist-development time, a determination is made of whether separation has occurred in each increment. This determination is made using respective random numbers weighted by the weighting parameters used in the fourth step. A sixth step is performed under the assumption that each molecule of the resist is separated from the layer of resist in each increment in which separation of resist molecules is going to occur. In the sixth step, for each such increment, the respective volume of separated resist molecules is determined using respective random numbers weighted based on the volume distribution calculated in the second step. In a seventh step, using random numbers, respective widths of the volumes of separated resist molecules are determined. Also calculated are the respective depths of the volumes determined in the sixth step. Finally, according to an array of the respective depths of the volumes, a line is extended connecting the depths. The line indicates a simulated profile of the resist surface after separation.
The method further can comprise the step, after the last step described above, of repeating the third through eighth steps as required until the total resist-development time is equal to a predetermined resist-development time. If the predetermined resist-development time has been reached, the simulation is ended. If not, the simulation returns to the third step.
The method further can comprise the step, after the eighth step described above, of estimating the profile of the pattern element after development of the resist.
According to another aspect of the invention, methods are provided for simulating the three-dimensional (xe2x80x9cbird""s-eyexe2x80x9d) profiles of developed resist corresponding to an exposed pattern element. The simulation includes a calculation based on the three-dimensional distribution of the rate of resist development. In a first step, with respect to a layer of the resist, data are input concerning the distribution of molecular weight and the mean density of the resist. In a second step, from the input data, a volume distribution of molecules of the resist is calculated. In a third step, an area of contact of a surface of the resist with a resist-developer solution is divided into increments desirably having equal respective areas. In a fourth step, based on a distribution of development rate for the resist, respective weighting parameters are assigned to each increment. In a fifth step, after a selected amount of resist-development time, a determination is made, using respective random numbers weighted using the weighting parameters used in the fourth step, of whether separation has occurred in each increment. A sixth step is performed under the assumption that each molecule of the resist is separated from the layer of resist in each increment in which separation of the resist molecules is going to occur. For each such increment the respective volume of separated resist molecules is determined using respective random numbers that are weighted based on the volume distribution calculated in the second step. In a seventh step, an assumption is made that each volume of separated resist molecules is shaped as a respective rectangular parallelepiped having a respective bottom surface with respective long and short sides and rotational angle. From the respective volumes of separated resist molecules determined in the sixth step, for each parallelepiped the ratio of the respective lengths of the long side and short side as well as the rotational angle are determined. Also, for each parallelepiped the areas of the respective bottom surfaces and the respective depth of the parallelepiped are calculated. In an eighth step, according to the respective bottom surface areas and depths, a line is extended indicating a profile of the resist surface after separation has occurred.
The method summarized above further can comprise the step, after the eighth step, of repeating the third through eighth steps as required until the total resist-development time is equal to a predetermined resist-development time.
According to conventional simulation methods, whenever a resist-development calculation is performed using the spatial distribution of the rate of resist development, the region of the resist that was the subject of the calculation was regarded as exhibiting a smooth, continuous body. Consequently, the results of the simulations did not account appropriately for edge roughness of pattern elements as imprinted into the resist. The present methods, on the other hand, reflect the separation of resist molecules that occurs during resist development. The present methods also are based on an assumption that each molecule of the resist is separated from the layer of resist in each region (increment) in which separation of the resist molecules is going to occur. As a result, the simulation results obtained with the present methods more closely approximate the behavior of actual developed resists as well as actual pattern-element profiles formed in such resists, including edge roughness. Thus, the present methods accurately predict effects of edge roughness on the respective profiles of pattern elements formed in the developed resist, as well as the limits on how narrowly a pattern element can be as formed in the developed resist. It is also possible, using the present methods, to calculate the optimum sizes of molecules of the resist material and to optimize the mean molecular weight or the distribution of molecular weight of the resist material.
The foregoing and additional features and advantages of the invention will be more readily apparent from the following detailed description, which proceeds with reference to the accompanying drawings.